I am not familiar with situation in other countries but here in Czechoslovakia it was quite clear.
Border regions - where the glassworks were mostly placed were connected to German "Reich" according to Munich's agreement between France, UK, Italy and Germany, so it that time it was not re-labeling or re-naming but really designation of country of origin - but as I wrote - typical it was in German language not in English. The international market was closed during the war, so I cannot see any rational reason to use English. Moreover the owners of the most glass factories in Haida region were German spoken CS citisens and connection to Germany in first years 1939/1940 was observed by them like positive and it satisfied their national wishes. The very special situation was with the properties owned by Jews, all had been confiscated and germanised. It had happened to Moser, for example.
Clearly is the situation described in Marcus Newhall's book.
The glass production during war was oriented to military needs rather than to parfum bottles, many factories had personal problems becouse men went to war. The rest part of Czechoslovakia was really occupied, German created there Protectorate and Slovakia had own state that colaborated with Germans. The glass industry had not same problems as regions directly under the German rule, Czech glassmakers that eskaped from parts of country annected by Germany had found jobs in inland. Note please that in 1940 had grounded Mr. Emanuel Beranek his glasswork in Skrdlovice, he was one from glassmakers who came from Haida (Novy Bor) region. His war production - so called "Skrdlovice antique" is very collectable now.
After the war was the Munich's agreement anullated and border regions re-connected to Czechoslovakia again. Unfortunately our ancestors had decided to "solve German problem" in Czechoslovakia "once and forever" and according to Potsdam's agreement they decided to drive out all German spoken Czechoslovakians, who were not able to proof, that they were anti-nazi active during war. So it has happened that the border regions were saddenly empty and were attacked by "gold-diggers" from other part of country. Some of factory owners were jailed by Czechoslovakians or Russians (Schlevogt, Riedel) and then expieled, tragical was fate of old Podbira who was killed by "revolution guard".
Czechoslovakia had lost many skilled glassmakers and logicaly these people continued in their work in new homes in Germany, mainly in Bavaria. So it is very problematic to speak about stolen marks or designs, the last century was horrible.